University of Twente Student Theses
A study on constellations using random graphs
Sleurink, J.K. (2021) A study on constellations using random graphs.
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| Abstract: | In this paper, we develop a mathematical model that attempts to describe constellations. We present a random graph model that generates links between two stars based on their brightness and the angular distance between them, weighed against the brightness of and distance to other stars. We use the model to determine whether there is a mathematical mechanism behind constellations. If a suitable mathematical mechanism is found, it could help quantify the performance of the human mind on visualising structures. We measure the performance of the model based on the overlap between links in the constellation and links generated by the model. We find that on average slightly less than half of the links overlap. We also find that adjusting the attenuation function that determines the influence of the angular distance between the stars on the probability that a link is generated does not affect the results. Generally, the model performs slightly better for smaller constellations. We conclude from the results that the specific model presented with the way we implemented it does not imply that there is a mathematical mechanism behind constellations. We suggest that the model could be improved by increasing the influence of the interference factor, or requiring the generated links to form a connected component. Additionally, the model can also be applied to all visible stars in a bounded area. |
| Item Type: | Essay (Bachelor) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics |
| Programme: | Applied Mathematics BSc (56965) |
| Link to this item: | https://purl.utwente.nl/essays/85930 |
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